Stability Analysis Using Quadratic Constraints for Systems With Neural Network Controllers

A method is presented to analyze the stability of feedback systems with neural network controllers. Two theorems are given prove asymptotic and compute an ellipsoidal innerapproximation region attraction (ROA). The first theorem addresses linear time-invariant systems, merges Lyapunov theory local (sector) quadratic constraints bound nonlinear activation functions in network. second allows system include perturbations such as unmodeled dynamics, slope-restricted nonlinearities, time delay, using integral constraint (IQCs) capture their input/output behavior. This turn for off-by-one IQCs refine description by capturing slope restrictions. Both results rely on semidefinite programming approximate ROA. illustrated networks trained stabilize a inverted pendulum well vehicle lateral dynamics actuator uncertainty.